# Both sides mean the same amount


## Access

Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

## Adult model

Right side 390+75=465;□=465−245=220. Substitution 245+220=465 and 390+75=465. The box is 220, not 465. Keep each original side intact.

## Child direction

Make a puzzle another person can check without guessing what the equals sign means. Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

## Common tangle

If 465 is entered in the box; check the roles and equivalent quantities, rather than memorising a printed answer.

## Day

58

## Different guided practice

For a fictional drawer 620−185=□+240: left 435, unknown 195, check 195+240=435. Invite the learner to compute the known side before undoing the other part.

## Check and teach the entry relationship

Check 12+3=10+5 as equal 15, then 12+□=10+5 gives 3. If = means next answer, use two named equal 15 bars and vary one decomposition.

## Hook

Make a puzzle another person can check without guessing what the equals sign means.

## Materials

Broad paper, labelled place-value/part-whole/number-line alternatives as suitable; optional familiar safe counters; usual communication. No hundreds of loose marks, purchases or physical handling required. Keep adult model and own work separate.

## Next ordinary teaching

If 465 is entered in the box, use 20+□=30+7: known side 37, missing 17. Guide 20+17=37; then invite 14+□=20+8 gives 14.

## Complete fictional source

An invented display equation is 245+□=390+75. Find the box value and check both sides.

## One own invitation

Solve 128+□=200+47 and check the two sides.

## Partial curriculum opportunity


1. AC9M4A01

2. AC9M4N06

## Purpose

Find an unknown when each side contains a calculation.

## Routes


1. 
### Access

Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

### Complete task

Solve 18+□=25+7, preserving both sides.

### Entry or access

Represent each entire side as a whole.

### Id

A

### Title

Small equality puzzle

### After own work: adult practice possibility

14; 18+14=32=25+7.


2. 
### Access

Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

### Complete task

Use 245+□=390+75. Create a readable substitution check.

### Entry or access

No balance-scale physical claim is needed.

### Id

B

### Title

Display equation

### After own work: adult practice possibility

220; both sides 465.


3. 
### Access

Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

### Complete task

Solve 2000−675=□+486. Show what is known first.

### Entry or access

Use a broad labelled two-side diagram.

### Id

C

### Title

Archive equality

### After own work: adult practice possibility

839; 1325=839+486.


## Session stages


1. 
### Instruction

Make a puzzle another person can check without guessing what the equals sign means. Read the source. Ask what the numbers count and the wanted quantity. Check 12+3=10+5 as equal 15, then 12+□=10+5 gives 3. If = means next answer, use two named equal 15 bars and vary one decomposition.

### Minutes suggestion

5

### Stage

Meet the job


2. 
### Instruction

Right side 390+75=465;□=465−245=220. Substitution 245+220=465 and 390+75=465. The box is 220, not 465. Keep each original side intact. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

### Minutes suggestion

10

### Stage

Teach one relationship


3. 
### Instruction

For a fictional drawer 620−185=□+240: left 435, unknown 195, check 195+240=435. Invite the learner to compute the known side before undoing the other part. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

### Minutes suggestion

15

### Stage

Guide then choose


4. 
### Instruction

Solve 128+□=200+47 and check the two sides. Receive an available response before staff key. If 465 is entered in the box, use 20+□=30+7: known side 37, missing 17. Guide 20+17=37; then invite 14+□=20+8 gives 14.

### Minutes suggestion

5

### Stage

Receive and choose tomorrow


## What to look for

Unknown 119 makes both full sides equal 247; explanation distinguishes box value from whole-side value.

## After own work: staff possibility

119; 128+119=247 and 200+47=247.

## Status

Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

## Title

Both sides mean the same amount